Phase noise reduction in an optical phase-locked loop is investigated using an acousto-optic actuator external to the laser cavity and primary stabilization lock. This method does not require modification of the laser cavity or primary lock and is compatible with continuous frequency tuning schemes for a laser locked to a femto-second frequency comb [J. Opt. Soc. Am. B 26, 1276 (2009) [CrossRef] ; Opt. Lett. 40, 4372 (2015) [CrossRef] ]. We achieve a cross-over frequency of 275 kHz and we demonstrate a single side band phase noise of at a 10 kHz offset. Using two independently tunable lasers equipped with this locking system, we demonstrate quantum state manipulation of ultra-cold dimers using stimulated Raman adiabatic passage.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Inducing stimulated Raman transitions in physical systems requires mutual phase coherence between two optical sources. Certain applications are particularly demanding with regard to the degree of phase coherence required, including quantum state control and quantum gate operations with trapped ions , quantum control of molecular states [2–6], electromagnetically induced transparency (EIT) [7,8], and atom interferometry [9,10]. In some cases, the two optical fields for the Raman transition can be derived from the same laser source using frequency shifting elements, and thus the detrimental effect of laser phase noise is minimized. When the frequency difference of the two fields exceeds the range of frequency shifting actuators, an optical phase-locked loop (OPLL) can be used to phase-lock two independent optical sources. OPLLs require a measurement of the optical phase (typically by heterodyne) and feedback to a frequency or phase correction actuator(s) placed inside [9,10] or outside the laser cavity [11,12] or both [13,14]. Unlike the intra-cavity options, the addition of external actuation does not require redesigning an existing laser cavity and can result in only modest optical power penalties ().
In this work, we explore and characterize the level of phase noise reduction that can be achieved with an external acousto-optic modulator (AOM) added to an existing pre-stabilization laser locking setup. Setting up this system is relatively simple and involves sampling the optical field of the laser field already locked to a frequency reference and using the external AOM to further reduce the phase noise of the optical field by fast electronic feedback to the voltage controlled oscillator (VCO) controlling the AOM. We demonstrate close to a factor of 2 shorter delay and correspondingly higher closed loop bandwidth for the AOM actuator than previous work [11,13–15] and provide a full characterization of the phase noise achieved across the entire suppression band revealing a transform limited linewidth (characteristic of a tightly locked OPLL) and a single side band (SSB) phase noise of below from 20 Hz to 130 kHz.
Key to our implementation is that the external AOM stabilization scheme measures and acts on the pre-stabilized laser field and is thus completely independent of the pre-stabilization locking setup. This choice avoids the complexity associated with constructing and optimizing multi-actuator locks—a process that typically involves custom loop filters and coupled feedback loops. In particular, our scheme enables us to independently optimize—with readily available off-the-shelf electronics—the performance and stability of both a low-bandwidth and high-dynamic-range lock and a high-bandwidth and low-dynamic-range AOM-based lock. This is advantageous because coupled feedback loops are inherently subject to compromises between stability and performance. In addition, we show that the locking VCO output can be used to simultaneously drive a second AOM, allowing fast intensity control of the phase-locked optical field while maximizing the amount of laser power available for the experiment. This option is useful when maximizing optical power is essential, and we provide phase noise measurements of the secondary field.
External AOMs have been used previously to provide laser phase noise suppression in conjunction with an external electro-optic modulator (EOM) to stabilize a dye laser , in conjunction with a cavity length tuning piezo-electric transducer (PZT) to stabilize a Nd:YAG laser  and in an independent feedback loop for phase noise suppression of a pre-stabilized dye laser equipped with an intracavity EOM and PZT . AOMs have also been used to suppress phase noise introduced by fiber distribution of pre-stabilized lasers for optical clock experiments (see, for example, ). Despite their prior demonstrations and standard use in some AOM laboratories as stabilization actuators, little information is available as to the level of phase noise suppression they provide across the entire suppression band. This work seeks to provide this information and to explore the limits of the phase noise correction possible with an AOM. Table 1 provides the locking bandwidth for different locking configurations and, where available, the power spectral density achieved at various offsets from the carrier inferred from an out-of-loop optical heterodyne and the reported resolution bandwidth.
Reference  does provide a measurement of the heterodyne beat signal up to 2 MHz from the carrier achieved by an external EOM AOM stabilizer applied to a dye laser phase-locked to a reference He–Ne laser. That work reports a heterodyne spectrum consistent with a noise power spectral density of at 100 kHz and reveals poor phase noise suppression at the crossover frequency between the EOM and AOM control (only below the carrier at 250 kHz). The authors attribute this to an uncompensated phase difference of the EOM and AOM at the crossover frequency.
Poor phase noise suppression due to uncompensated actuator phase differences is generic to control applications that include multiple actuators responsible for feedback correction in different frequency bands, and simultaneously achieving stability and optimal performance can be a very challenging design problem. In particular, stability in such coupled systems usually requires the crossover frequency to be well below the resonance frequency (or equivalently the inverse delay time) of the slow actuator and thus limit the tightness of the lock. In some cases, simply cascading multiple servo loops with the slower actuator servo receiving as its error signal the output of the faster actuator servo is sufficient to obtain stability, but this approach does not necessarily result in the optimal phase noise suppression.
A solution that ensures stability and performance is to apply the stabilization stages independently and serially to the optical field, creating a pre-stabilized optical field that is further stabilized by additional servo loops. While this solution may be impractical in cases where the error signal generation is difficult or costly (e.g., if the external reference is a single cavity), it can be easily applied in cases where multiple cavities are available (as shown in Ref. ) or when the comparison is with a stable reference oscillator and the error signal comes from a heterodyne beat note, as in this work. Here we use an external AOM to achieve an optical phase lock of a pre-stabilized Ti:sapphire laser to a femtosecond frequency comb. We show that this method is compatible with previously demonstrated schemes for realizing continuous tuning of a laser locked to a frequency comb [16,17], and using two independently tunable lasers equipped with this locking system, we demonstrate quantum state manipulation of ultra-cold dimers using stimulated Raman adiabatic passage (STIRAP).
2. SYSTEM DESIGN
A schematic for the system with an additional external AOM-based phase-locked loop is shown in Fig. 1 where (a) shows the entire system consisting of the laser to be stabilized, optical reference, locking branch, and experiment branch. Subfigures (b) and (c) of Fig. 1 show the phase/frequency correction actuator and the associated locking electronics, respectively.
In our experiment, the frequency of a Ti:sapphire laser (TS1) is pre-stabilized by electronic feedback to a piezoelectric transducer controlling the cavity length. The PZT lock uses light sampled directly out of the laser and is thus independent and de-coupled from the AOM-based lock that follows. A phase-frequency discriminator (PFD) is used instead of a mixer to extend the capture range of the PZT lock. Pre-stabilization eliminates DC frequency errors and minimizes the dynamic range requirements of the AOM-based lock. The decoupling of the two locks allows them to be independently optimized for performance and stability and avoids complications associated with designing customized loop filters for coupled feedback loops.
The phase noise of the pre-stabilized light is characterized by the power spectrum of the heterodyne beat-note between it and a fiber-based frequency comb (FFC), described below and labeled PZT in Fig. 2. The phase noise is further reduced using feedback to an AOM actuator as shown in Fig. 1(b). To achieve a high closed loop bandwidth, we focus the input beam ( intensity diameter of 1.5 mm) with a 300 mm lens and minimize the acoustic wave propagation delay by translating the AOM such that the beam is incident on the crystal as close as possible to the source. This results in a propagation delay of 135 ns and a 10%–90% rise time of 80 ns. We maximize the actuator dynamic range and minimize residual amplitude variation from fiber coupling the deflected beam by placing a collimating lens as close to the AOM as possible. Here, 200 mm was chosen because of the need to block the undiffracted beam. The AOM deflected beam is re-collimated and is, to first order, parallel to the lens optic axis independent of the deflection angle (i.e., AOM frequency). As a result, the power through the fiber is almost constant over a driving frequency range of several megahertz (MHz) and drops to 80% at away from our center frequency of 63 MHz. As shown in Fig. 1(b), the shifted beam is combined with a second laser (entering the L2-in port), passed through a Glan–Thompson (GT) polarizer, and coupled into a single-mode, polarization maintaining (SM/PM) fiber to ensure mode overlap.
The heterodyne beat is detected on a photodiode in block Fig. 1(c). In the AOM locking branch, we measure the heterodyne beat of TS1 entering the L1-in port with the FFC entering the L2-in port. The FCC is a self-referenced frequency comb generated by an erbium-doped fiber laser with a center frequency of 1550 nm. The oscillator mode-locking is based on nonlinear polarization rotation and produces sub-100 fs pulses at a repetition rate of 125 MHz. The comb light is frequency doubled using a periodically poled lithium niobate (PPLN) crystal to match the frequency range of our two tunable cw Ti:sapphire lasers. More details of the comb and locking electronics can be found in . In block Fig. 1(b) of the experiment branch we combine TS1 with light from a second TS laser (TS2) or the FFC (not shown) to diagnose the phase noise of the light generated for the STIRAP experiment.
In Fig. 1(c), a mixer generates an error signal by combining a reference RF signal and the filtered and amplified heterodyne beat note between the frequency-doubled (via the PPLN crystal) FFC and TS1. The output of the VCO (Mini-Circuits ROS-70-119+), whose control input is driven by a Vescent Photonics D2-125 loop filter, is used to issue a correction signal for the optical field. The VCO output is split and amplified by two power amplifiers (PA). The amplified signals (RF1 and RF2) are sent to the locking branch AOM and to the experiment branch AOM, generating a copy of the corrected light field. The amplitude of the RF sent to the experiment arm AOM can be independently controlled via a voltage controlled attenuator (VCA) without perturbing the lock. We achieve pulse shaping in an open loop configuration using an SRS DS345 arbitrary waveform generator. For applications that require further reduction of the amplitude noise, a stabilization control loop can be added.
To perform STIRAP, a second Ti:sapphire (TS2) laser is used. The arrangement is almost identical, but includes a double pass AOM immediately after the laser block, which permits scanning the laser frequency without changing the FFC’s repetition rate (see  for details). For the diagnostics measurement in Fig. 3 as well as the STIRAP measurement in Fig. 4, TS2 is combined with TS1 in block Fig. 1(b) of the experiment section.
Out-of-loop measurements of the power spectrum and single-sideband phase noise of the heterodyne beat note between a locked Ti:sapphire laser and the FFC are shown in Fig. 2 under different locking conditions. The SSB phase noise measurements were made using the Agilent 85671A Phase Noise Utility on an HP8563E RF spectrum analyzer. Each plot represents the average of 10 measurements without filtering or smoothing. The specified noise floor of the HP8563E is from 10 to 400 Hz and drops below beyond 1 kHz.
Characteristic of a tightly locked OPLL system, we observe a transform limited linewidth. In particular, using a sampling scope with a large storage capacity, we confirmed that the apparent linewidth is 0.1 Hz (and thus unresolved and well below 0.1 Hz) for a 10 s sampling duration. By using identical AOM actuators for the experiment () and locking () branches and by carefully matching their propagation delays (as discussed above), we achieve a level of phase noise suppression for the experiment branch that is similar to the locking branch above 3 kHz. For example, at a 10 kHz offset, the SSB phase noise is and for the locking branch and experiment branch, respectively. We confirmed that the additional 4 dB of phase noise in the experiment branch at frequencies between 5 and 100 kHz offset is produced by voltage noise at the input of the VCA from the DS345.
The markedly larger phase noise of the measurement below 3 kHz results from a combination of voltage noise at the input of the VCA from the DS345 and from vibrations of optical elements that are not common to both the and paths. In particular, the phase noise spurs between 100 Hz and 3 kHz appear to result from voltage noise at the input of the VCA from the DS345 while the rise in the phase noise baseline starting just below 1 kHz and becoming quite pronounced (more than a 20 dB rise above the locking arm) below 100 Hz is due to vibrations of mirrors not common to the experiment and locking paths. In short, low-frequency phase noise generated by mirror vibrations that are exclusive to the path is not corrected, and, since we use a copy of the correction signal for the path as the correction signal path, we write low-frequency phase noise associated with vibrations of optical elements in the L path onto the field at the output of the path. Similar low-frequency noise is evident in the heterodyne beat measurement between TS1 and TS2 (see Fig. 3) obtained using the fields from the experiment branches.
While this has a negligible effect on the STIRAP efficiency demonstrated here, other applications including atom interferometry are more sensitive to noise at these frequencies [9,10]. Using a lower noise voltage source for the VCA, rearranging the optical components, using higher quality optomechanical mounts, and adding acoustic dampeners would reduce this phase noise generated after the lock. Alternatively, if loss of optical power is not an issue, all of the light from the laser could be channeled through the path and then a second AOM could be used to send this light directly to the experiment and to independently control its intensity. In this case, the mutual phase noise between TS1 and TS2 would be significantly lower than we observe in Fig. 3. Ultimately, the system’s performance is limited by the finite response time of the AOMs.
4. APPLICATION TO STIRAP
An application of our Raman laser system is quantum state manipulation of an ensemble of ultra-cold dimers. We realize coherent population transfer from a loosely bound Feshbach molecular state (the is an s-wave molecule, , with both spin singlet and triplet character) to a more deeply bound state where is the , level of the triplet potential. The intermediate state was the level in the triplet potential . The Feshbach molecules are formed by first laser cooling atoms in a Zeeman slower loaded magneto-optical trap (MOT) , then transferring them into an optical dipole trap  and performing forced evaporative cooling at 755 G where Feshbach molecules form once the ensemble temperature drops below the binding energy. Starting from results on photo-association to states in the potential  and dark-state spectroscopy to the state , we performed spectroscopy of the same levels at 755 G as a prerequisite for the population transfer we demonstrate here. The Feshbach molecule number after a forward and reverse STIRAP pulse sequence is shown in Fig. 4. The total round-trip efficiency is 50% and could be improved by optimizing the shape and duration of the pulses used for the transfer as well as the waists of the photo-association beams striking the atoms. We observed that the STIRAP efficiency was unchanged with and without the fast lock engaged even when we went to longer exposure times. We believe this is because the decoherence during STIRAP is not limited by the phase noise of the Raman lasers but by the finite lifetime of the deeply bound molecules formed during STIRAP. A detailed study of the collision dynamics of molecules in various states in the potential will be published separately.
In this paper, we demonstrate phase noise reduction using an external AOM for mutually tunable Ti:sapphire lasers phase-locked to an FFC. We add feedforward arms (with similar performance) whose amplitudes can be arbitrarily shaped without disturbing the phase lock. Alternatively, if loss of optical power is not an issue, all of the light from the laser could be channeled through the lock path, and a second AOM could be used to send this light directly to the experiment and to independently control its intensity. We use this system to perform quantum state control in dimers using STIRAP. While we were unable to achieve phase noise reduction down to the shot noise level because of the inherent acoustic delay of the AOM actuators used and because of the limited configuration options of our loop filters, we believe that increasing the closed loop bandwidth of the OPLL is possible. This could be achieved with AOMs that do not require angle tuning and consequently have a significantly shorter acoustic delay [22,23] or with custom loop filters whose transfer functions are optimized for this plant.
Natural Sciences and Engineering Research Council of Canada (NSERC) (CRSNG); Canada Foundation for Innovation (CFI); Center for Research on Ultra-Cold Systems (CRUCS); Deutsche Forschungsgemeinschaft (DFG).
This work was done under the auspices of the Center for Research on Ultra-Cold Systems (CRUCS). We wish to thank Sudip Shekhar, Arthur K. Mills, and Daniel A. Steck for sharing their insights into optimizing the performance of PLLs. G. P., J. S., D. U., E. F, and K. D. acknowledge support from the DFG within the GRK 2079/1 program.
1. D. J. Wineland, C. Monroe, W. M. Itano, D. Leibfried, B. E. King, and D. M. Meekhof, “Experimental issues in coherent quantum-state manipulation of trapped atomic ions,” J. Res. Natl. Inst. Stand. Technol. 103, 259–328 (1998).
2. K. Winkler, F. Lang, G. Thalhammer, P. V. Straten, R. Grimm, and J. H. Denschlag, “Coherent optical transfer of Feshbach molecules to a lower vibrational state,” Phys. Rev. Lett. 98, 1–4 (2007). [CrossRef]
3. K. K. Ni, S. Ospelkaus, M. H. De Miranda, A. Pe’er, B. Neyenhuis, J. J. Zirbel, S. Kotochigova, P. S. Julienne, D. S. Jin, and J. Ye, “A high phase-space-density gas of polar molecules,” Science 322, 231–235 (2008). [CrossRef]
4. F. Lang, K. Winkler, C. Strauss, R. Grimm, and J. H. Denschlag, “Ultracold triplet molecules in the rovibrational ground state,” Phys. Rev. Lett. 101, 1–4 (2008). [CrossRef]
5. J. G. Danzl, E. Haller, M. Gustavsson, M. J. Mark, R. Hart, N. Bouloufa, O. Dulieu, H. Ritsch, and H.-C. Nägerl, “Quantum gas of deeply bound ground state molecules,” Science 321, 1062–1066 (2008). [CrossRef]
6. J. G. Danzl, M. J. Mark, E. Haller, M. Gustavsson, R. Hart, J. Aldegunde, J. M. Hutson, and H. C. Nägerl, “An ultracold high-density sample of rovibronic ground-state molecules in an optical lattice,” Nat. Phys. 6, 265–270 (2010). [CrossRef]
7. D. Höckel, M. Scholz, and O. Benson, “A robust phase-locked diode laser system for EIT experiments in cesium,” Appl. Phys. B 94, 429–435 (2009). [CrossRef]
8. A. M. Marino and C. Stroud Jr., “Phase-locked laser system for use in atomic coherence experiments,” Rev. Sci. Instrum. 79, 013104 (2008). [CrossRef]
9. J. Le Gouët, J. Kim, C. Bourassin-Bouchet, M. Lours, A. Landragin, and F. Pereira Dos Santos, “Wide bandwidth phase-locked diode laser with an intra-cavity electro-optic modulator,” Opt. Commun. 282, 977–980 (2009). [CrossRef]
10. H. Müller, S.-W. Chiow, Q. Long, and S. Chu, “Phase-locked, low-noise, frequency agile titanium: sapphire lasers for simultaneous atom interferometers,” Opt. Lett. 31, 202–204 (2006). [CrossRef]
11. M. Zhu and J. L. Hall, “Stabilization of optical phase/frequency of a laser system: application to a commercial dye laser with an external stabilizer,” J. Opt. Soc. Am. B 10, 802–816 (1993). [CrossRef]
12. S. Wey Chiow, S. Herrmann, H. Müller, and S. Chu, “6 W, 1 kHz linewidth, tunable continuous-wave near-infrared laser,” Opt. Express 17, 5246–5250 (2009). [CrossRef]
13. J. Ye and J. L. Hall, “Optical phase locking in the microradian domain: potential applications to NASA spaceborne optical measurements,” Opt. Lett. 24, 1838–1840 (1999). [CrossRef]
14. B. C. Young, F. C. Cruz, W. M. Itano, and J. C. Bergquist, “Visible lasers with subhertz linewidths,” Phys. Rev. Lett. 82, 3799–3802 (1999). [CrossRef]
15. M. J. Martin, “Quantum metrology and many-body physics: pushing the frontier of the optical lattice clock,” Ph.D. thesis (University of Colorado, 2013).
16. A. K. Mills, Y.-F. Chen, K. W. Madison, and D. J. Jones, “Widely tunable, single-mode optical frequency synthesizer with a 100 kHz uncertainty,” J. Opt. Soc. Am. B 26, 1276–1280 (2009). [CrossRef]
17. W. Gunton, M. Semczuk, and K. W. Madison, “Method for independent and continuous tuning of n lasers phase-locked to the same frequency comb,” Opt. Lett. 40, 4372–4375 (2015). [CrossRef]
18. M. Semczuk, X. Li, W. Gunton, M. Haw, N. S. Dattani, J. Witz, A. K. Mills, D. J. Jones, and K. W. Madison, “High-resolution photoassociation spectroscopy of the 6Li23Σ g + state,” Phys. Rev. A 87, 052505 (2013). [CrossRef]
19. W. Bowden, W. Gunton, M. Semczuk, K. Dare, and K. W. Madison, “An adaptable dual species effusive source and Zeeman slower design demonstrated with Rb and Li,” Rev. Sci. Instrum. 87, 043111 (2016). [CrossRef]
20. W. Gunton, M. Semczuk, and K. W. Madison, “Realization of BEC-BCS-crossover physics in a compact oven-loaded magneto-optic-trap apparatus,” Phys. Rev. A 88, 023624 (2013). [CrossRef]
21. M. Semczuk, W. Gunton, W. Bowden, and K. W. Madison, “Anomalous behavior of dark states in quantum gases of Li6,” Phys. Rev. Lett. 113, 055302 (2014). [CrossRef]
22. R. T. Weverka and K. H. Wagner, “Wide-angular aperture acousto-optic Bragg cell,” Proc. SPIE 1562, 66–72 (1991). [CrossRef]
23. J. Xu, R. T. Weverka, and K. H. Wagner, “Wide angular aperture lithium niobate acousto-optic Bragg cells,” Proc. SPIE 2240, 96–108(1994). [CrossRef]